Pendulum attached to a vibrating point: Semi-analytical solution by optimal and modified homotopy perturbation method
A simple pendulum of length (b) and bob mass (m) attached to point (O) is considered and investigated. The point (O) is oscillating vertically according to the relation (qocosΩt), where qo and Ωare amplitude and angular frequency of the external agent, respectively. The presence of time dependent os...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-01-01
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| Series: | Alexandria Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016824012493 |
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| author | Tapas Roy Aya Soqi Dilip K. Maiti Rania Wannan Jihad Asad |
| author_facet | Tapas Roy Aya Soqi Dilip K. Maiti Rania Wannan Jihad Asad |
| author_sort | Tapas Roy |
| collection | DOAJ |
| description | A simple pendulum of length (b) and bob mass (m) attached to point (O) is considered and investigated. The point (O) is oscillating vertically according to the relation (qocosΩt), where qo and Ωare amplitude and angular frequency of the external agent, respectively. The presence of time dependent oscillating term makes the governing equation is not solvable analytically. An attempt was to explore the application of optimal and modified homotopy perturbation method (OM-HPM) as a powerful semi-analytical tool for solving the oscillatory problem which exhibiting regular and irregular oscillation for some parameter set. Furthermore, the analytical expressions in series form, which is very close to the numerical solution of Runge-Kutta method is obtained. In addition, the analytical expression for the amplitude and the frequency of the oscillations for two cases: simple regular oscillation and the irregular oscillation is computed. Finally, the simplicity of the obtained solutions facilities a clear understanding, and the OM-HPM offer a robust and efficient analytical tool to obtain series based analytical solution for such kind of problems. |
| format | Article |
| id | doaj-art-008f308aa86541ecaabedcf2f8c9234e |
| institution | Kabale University |
| issn | 1110-0168 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj-art-008f308aa86541ecaabedcf2f8c9234e2025-01-18T05:03:42ZengElsevierAlexandria Engineering Journal1110-01682025-01-01111396403Pendulum attached to a vibrating point: Semi-analytical solution by optimal and modified homotopy perturbation methodTapas Roy0Aya Soqi1Dilip K. Maiti2Rania Wannan3Jihad Asad4Department of Applied Mathematics, Vidyasagar University, Midnapur, WB 721102, IndiaDep. of Applied Mathematics, Palestine Technical University- Kadoorie, Tulkarm P 305, PalestineDepartment of Applied Mathematics, Vidyasagar University, Midnapur, WB 721102, IndiaDep. of Applied Mathematics, Palestine Technical University- Kadoorie, Tulkarm P 305, PalestineDep. of Physics, Palestine Technical University, Kadoorie, Tulkarm P 305, Palestine; Corresponding author.A simple pendulum of length (b) and bob mass (m) attached to point (O) is considered and investigated. The point (O) is oscillating vertically according to the relation (qocosΩt), where qo and Ωare amplitude and angular frequency of the external agent, respectively. The presence of time dependent oscillating term makes the governing equation is not solvable analytically. An attempt was to explore the application of optimal and modified homotopy perturbation method (OM-HPM) as a powerful semi-analytical tool for solving the oscillatory problem which exhibiting regular and irregular oscillation for some parameter set. Furthermore, the analytical expressions in series form, which is very close to the numerical solution of Runge-Kutta method is obtained. In addition, the analytical expression for the amplitude and the frequency of the oscillations for two cases: simple regular oscillation and the irregular oscillation is computed. Finally, the simplicity of the obtained solutions facilities a clear understanding, and the OM-HPM offer a robust and efficient analytical tool to obtain series based analytical solution for such kind of problems.http://www.sciencedirect.com/science/article/pii/S1110016824012493Pendulum oscillationDamped–Harmonic oscillationsSeries solutionOptimal Homotopy perturbation methodVibrational dynamics |
| spellingShingle | Tapas Roy Aya Soqi Dilip K. Maiti Rania Wannan Jihad Asad Pendulum attached to a vibrating point: Semi-analytical solution by optimal and modified homotopy perturbation method Alexandria Engineering Journal Pendulum oscillation Damped–Harmonic oscillations Series solution Optimal Homotopy perturbation method Vibrational dynamics |
| title | Pendulum attached to a vibrating point: Semi-analytical solution by optimal and modified homotopy perturbation method |
| title_full | Pendulum attached to a vibrating point: Semi-analytical solution by optimal and modified homotopy perturbation method |
| title_fullStr | Pendulum attached to a vibrating point: Semi-analytical solution by optimal and modified homotopy perturbation method |
| title_full_unstemmed | Pendulum attached to a vibrating point: Semi-analytical solution by optimal and modified homotopy perturbation method |
| title_short | Pendulum attached to a vibrating point: Semi-analytical solution by optimal and modified homotopy perturbation method |
| title_sort | pendulum attached to a vibrating point semi analytical solution by optimal and modified homotopy perturbation method |
| topic | Pendulum oscillation Damped–Harmonic oscillations Series solution Optimal Homotopy perturbation method Vibrational dynamics |
| url | http://www.sciencedirect.com/science/article/pii/S1110016824012493 |
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